Problem Solving: Consecutive Integers Chapter 1 Section 1.8

Objective Students will write equations to represent relationships among integers

Concept When you want to be served at a bakery, a deli, or a pizza parlor you often must take a number. The numbers help the clerks keep track of who is next in line. When you count by ones from any number in the set of integers, you obtain consecutive integers. Example: -2, -1, 0, 1, 2 are five consecutive integers

Concept When dealing with consecutive integers variables may be used. Even if variables are used, you still count by ones to write consecutive integers.

Example An integer is represented by n Write the next three integers after n Write the integer than immediately precedes n Write an equation that states that the sum of four consecutive integers, starting with n, is 66

Concept An integer that is the product of 2 and any other integer is an even integer. … , -6, -4, -2, 0, 2, 4, 6, … An odd integer is an integer that is not even. … , -5, -3, -1, 1, 3, 5, …

Concept If you count by twos beginning with any even integer, you obtain consecutive even integers. Example: 8; 8 + 2 or 10; 10 + 2 or 12 8, 10, 12

Concept If you count by twos beginning with an odd integer, you obtain consecutive odd integers. Example: 9; 9 + 2 or 11; 11 + 2 or 13 9, 11, 13

Concept Even or odd consecutive integers in order from least to greatest: n, n + 2, n + 4 An even or odd number is determined by what you start with

Example Write an equation to represent the given relationship among integers The sum of two consecutive integers is 93 The sum of three consecutive integers is 192

Example The product of two consecutive even integers is 120 The largest of three consecutive even integers is three times the smallest

Example 5. Twice the smaller of two consecutive odd integers is seven more than the larger

Questions

Assignment Worksheet